In the prediction of time series, or also in the modeling of processes with the aid of neural networks, expert knowledge is often ignored. Since, however, in many cases experts can be found for the respective problematic who are in a position to express their knowledge in the form of fuzzy rules, what are called neuro-fuzzy systems are used for predicting time series or for modeling processes, whereby fuzzy systems and neural networks, with their respective characteristic properties, are combined with one another.
A fuzzy system specified by means of rules is thereby standardly translated into a neural network equivalent to the rules, and the neural network is optimized on the basis of training data. The optimized neural network is then again mapped onto fuzzy rules, whereby knowledge concerning the now-optimized system is extractable for an expert. This would not be possible given the exclusive use of neural networks.
Basic principles of neuro-fuzzy systems are known for example from document, R. Kruse et al., Neuronale Fuzzy-Systeme, Spektrum der Wissenschaft, S. 34-41, June 1995.
An overview of various learning methods for neural networks, for example monitored learning methods or unmonitored learning methods, are known from document, J. Hertz et al., Introduction to the Theory of Neural Computation, Lecture Notes Volume I, Addison Wesley Publishing Company, ISBN 0-201-51560-1, 1995.
Methods for removing (pruning) or, respectively, reviving (growing) weights and/or neurons of a neural network are known for example from document, C. Bishop, Neuronal Networks for Pattern Recognition, Clarendon Press, Oxford, ISBN 0-198-538-642, pp.353-364, 1995 and document, A. Gail et al., Rule Extraction: From Neural Architecture to Symbolic Representation, Connection Science, vol. 7, no.1, pp. 3-27, 1995.
In addition, it is known from document, R. Neuneier and H. G. Zimmermann, A Semantic-Preserving Learning Algorithm for Neuro-Fuzzy Systems with Applications to Time Series Prediction, Proceedings of the ICANN Workshop "Banking, Finance and Insurance," Paris, pp. 1-5, 1995, to use semantics-preserving learning algorithms for the training of the neural network of a neuro-fuzzy system, so that the new rules of the fuzzy rule set continue to make correct and useful statements.
In addition, it is also known from document, R. Neuneier and H. G. Zimmermann, A Semantic-Preserving Learning Algorithm for Neuro-Fuzzy Systems with Applications to Time Series Prediction, Proceedings of the ICANN Workshop "Banking, Finance and Insurance," Paris, pp.1-5, 1995, to prune entire rules of the rule set in the optimization of the neural network of a neuro-fuzzy system.
In addition, what is called an early-stopping method is also known from document, W. Finnoff et al., Improving Generalization by Nonconvergent Model Selection Methods, Neural Networks, no. 6, 1992, for the pruning or, respectively, growth of the weights and/or neurons of a neural network.
In the document, H. Hensel et al., Optimierung von Fuzzy-Control mit Hilfe Neuronaler Netze, atp, Automatisierungstechnische Praxis, vol. 37, no. 11, pp. 40-48, 1995, an overview concerning the optimization of fuzzy control with the aid of neural networks is specified.
From, J. Hollatz, Integration von regelbasiertem Wissen in neuronale Netze, Dissertation Institut fur Informatik, Technische Universitat Munchen, pp. 35-58, 1993, an overview is known concerning the design of rules and the transformation of rules in neural networks.
The pruning of entire rules in a fuzzy rule set has the disadvantage that the granularity of the optimization of the fuzzy rule set is very rough. For this reason, the precision of the fuzzy rule set obtained is relatively low. The results achieved with the optimized fuzzy rule set are also imprecise with this known method.